# The Stochastic Structural Modulations in Collapsing Maccari’s Model Solitons

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## Abstract

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## 1. Introduction

- (i)
- $\Xi \left(t\right)$; $t\ge 0$ is a continuous function of t,
- (ii)
- $\Xi \left(r\right)-\Xi \left(t\right)$ is independent of increments, for $r<t$,
- (iii)
- $\Xi \left(t\right)-\Xi \left(r\right)$ follows a normal distribution with mean 0; variance $t-r$.

## 2. Description of the Method

#### 2.1. Family 1

#### 2.2. Family 2

#### 2.3. Family 3

## 3. Solutions of MS

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Trajectory of exact solution (26).

**Figure 3.**Trajectory of solution (19).

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**MDPI and ACS Style**

Abdelwahed, H.G.; Alsarhana, A.F.; El-Shewy, E.K.; Abdelrahman, M.A.E. The Stochastic Structural Modulations in Collapsing Maccari’s Model Solitons. *Fractal Fract.* **2023**, *7*, 290.
https://doi.org/10.3390/fractalfract7040290

**AMA Style**

Abdelwahed HG, Alsarhana AF, El-Shewy EK, Abdelrahman MAE. The Stochastic Structural Modulations in Collapsing Maccari’s Model Solitons. *Fractal and Fractional*. 2023; 7(4):290.
https://doi.org/10.3390/fractalfract7040290

**Chicago/Turabian Style**

Abdelwahed, H. G., A. F. Alsarhana, E. K. El-Shewy, and Mahmoud A. E. Abdelrahman. 2023. "The Stochastic Structural Modulations in Collapsing Maccari’s Model Solitons" *Fractal and Fractional* 7, no. 4: 290.
https://doi.org/10.3390/fractalfract7040290